Complex physical–chemical interactions between clay particles including the van der Waals force control the macroscopic behaviors of clay. The calculation of van der Waals force is essential in the discrete element method (DEM) that has been widely used to enhance the understanding of the behavior of clay. Due to its high computational efficiency, a plate-wall model developed in the literature was adopted to obtain the van der Waals force between the neighboring clay particles approximately in the published DEM simulations. However, different choices of the ideal wall result in different magnitudes as well as directions of total van der Waals forces. To investigate the effect, a new rigorous plate-plate model was put forward and solved using an optimized Cotes integration method. Based on the comparison between the calculated results based on plate-wall and plate-plate model, the above effect was analyzed for the cases of face-face, edge-edge and edge-face contact types. Then, necessary advice for the reasonable use of the ideal-wall model was given accordingly.

The knowledge of nanoscale mechanical properties of montmorillonite (MMT) with various compensation cations upon hydration is essential for many environmental engineering-related applications. This paper uses a Molecular Dynamics (MD) method to simulate nanoscale elastic properties of hydrated Na-, Cs-, and Ca-MMT with unconstrained system atoms. The variation of basal spacing of MMT shows step characteristics in the initial crystalline swelling stage followed by an approximately linear change in the subsequent osmotic swelling stage as the increasing of interlayer water content. The water content of MMT in the thermodynamic stable-state conditions during hydration is determined by comparing the immersion energy and hydration energy. Under this stable hydration state, the nanoscale elastic properties are further simulated by the constant strain method. Since the non-bonding strength between MMT lamellae is much lower than the boning strength within the mineral structure, the in-plane and out-of-plane strength of MMT has strong anisotropy. Simulated results including the stiffness tensor and linear elastic constants based on the assumption of orthotropic symmetry are all in good agreement with results from the literature. Furthermore, the out-of-plane stiffness tensor components of C₃₃, C₄₄, and C₅₅ all fluctuate with the increase of interlayer water content, which is related to the formation of interlayer H-bonds and atom-free volume ratio. The in-plane stiffness tensor components C₁₁, C₂₂, and C₁₂ decrease nonlinearly with the increase of water content, and these components are mainly controlled by the bonding strength of mineral atoms and the geometry of the hydrated MMT system. Young’s modulus in all three directions exhibits a nonlinear decrease with increasing water content.

Effects of impurity gases on interfaces of the hydrogen-water-decane three-phase system: A square gradient theory investigation

Interfacial tensions in the H₂ + H₂O + C₁₀H₂₂ 3-phase system at various temperatures and pressures.

The coefficient of earth pressure at rest (K₀) for normally consolidated clays increases nonlinearly with increasing consolidation pressure toward a steady value under high pressure rather than remaining constant. Analytical expressions for evaluating pressure-dependent K₀ were derived from three representative critical state soil models: modified Cam-clay model (MCC), original Cam-clay model (OCC), and clay and sand model (CASM). In formulations, the authors relaxed a well-adopted assumption that stress ratio is kept constant during one-dimensional (1D) compression. It is found that the constant stress ratio, corresponding to the well-adopted assumption, is essentially a limit value of the stress ratio as predicted by MCC and CASM under high pressure during 1D compression. The predicted relationship between K₀ and consolidation pressure is significantly affected by the critical state stress ratio. Without considering the effect of high pressure, the value of K₀ may be considerably underestimated. The results predicted by the proposed formula based on CASM agree well with experimental data, showing the capability of this formula for predicting pressure-dependent K₀.

The fluid–solid interfacial tension is of great importance to many applications including the geological storage of greenhouse gases and enhancing the recovery of geo-resources, but it is rarely studied. Extensive molecular dynamics simulations are conducted to calculate fluid–solid interfacial properties in H2O + gas (H2, N2, CH4, and CO2) + rigid solid three-phase systems at various temperatures (298–403 K), pressures (0–100 MPa), and wettabilities (hydrophilic, neutral, and hydrophobic). Our results on the H2O + solid system show that vapor–solid interfacial tension should not be ignored in cases where the fluid–solid interaction energy is strong or the contact angle is close to 90°. As the temperature rises, the magnitude of H2O’s liquid–solid interfacial tension declines because the oscillation of the interfacial density/pressure profile weakens at high temperatures. However, the magnitude of H2O vapor–solid interfacial tension is enhanced with temperature due to the stronger adsorption of H2O. Moreover, the H2O–solid interfacial tension in H2O + gas (H2 or N2) + solid systems is weakly dependent on pressure, while the pressure effects on H2O–solid interfacial tensions in systems with CH4 or CO2 are significant. We show that the assumption of pressure independent H2O–solid interfacial tensions should be cautiously applied to Neumann’s method for systems containing non-hydrophilic surfaces with strong gas–solid interaction. Meanwhile, the magnitude of gas–solid interfacial tension increases with pressure and gas–solid interaction. High temperatures generally decrease the magnitude of gas–solid interfacial tensions. Further, we found that the increment of contact angle due to the presence of gases follows this order: H2 < N2 < CH4 < CO2.